In case of indifference curve of two goods X and Y, as consumption of X increases:
Understanding Indifference Curves and MRS
An indifference curve represents all the combinations of two goods (in this case, goods X and Y) that provide a consumer with the same level of satisfaction or utility. This means that a consumer is indifferent between any point on the same indifference curve.
The slope of the indifference curve at any point measures the rate at which the consumer is willing to substitute one good for another while maintaining the same level of utility. This rate is known as the Marginal Rate of Substitution (MRS).
Defining Marginal Rate of Substitution (MRS)
The Marginal Rate of Substitution of X for Y ($MRS_{XY}$) is the amount of good Y that a consumer is willing to give up to get one additional unit of good X, while remaining on the same indifference curve.
Mathematically, $MRS_{XY}$ is represented by the absolute value of the slope of the indifference curve:
$\text{MRS}_{XY} = \left| \frac{\Delta Y}{\Delta X} \right|$
Here, $\Delta Y$ is the change in the quantity of good Y and $\Delta X$ is the change in the quantity of good X.
MRS and Consumption of Goods
Consider moving along an indifference curve from left to right. As we move to the right, the consumption of good X increases, and the consumption of good Y decreases (since the curve is downward sloping for normal goods).
A fundamental characteristic of typical indifference curves is that they are convex to the origin. This convexity is based on the principle of the Law of Diminishing Marginal Rate of Substitution.
Law of Diminishing Marginal Rate of Substitution
The Law of Diminishing MRS states that as a consumer consumes more and more of one good (say, good X), the amount of the other good (good Y) that they are willing to give up to get an additional unit of good X decreases. In other words, the consumer's willingness to substitute Y for X diminishes as they increase their consumption of X.
Let's illustrate this:
- When a consumer has a lot of good Y and only a little of good X, they are willing to give up a relatively large amount of Y to get an extra unit of X because X is scarce relative to Y, and the marginal utility of X is high.
- As the consumer consumes more of X and less of Y, X becomes less scarce, and the marginal utility of consuming an additional unit of X decreases relative to Y. Therefore, they are willing to give up less and less of Y to obtain another unit of X.
This implies that as the consumption of X increases along an indifference curve, the slope of the indifference curve (in absolute terms, which is the MRS) becomes flatter. A flatter slope means the value of $MRS_{XY}$ is decreasing.
Analyzing the Options
Based on the Law of Diminishing Marginal Rate of Substitution:
- As consumption of X increases along an indifference curve, the consumer is willing to give up a decreasing amount of Y for each additional unit of X.
- This directly translates to the $MRS_{XY}$ decreasing.
Let's look at the options:
- $MRS_{XY}$ increases: This contradicts the Law of Diminishing MRS and the typical convex shape of indifference curves.
- $MRS_{XY}$ decreases: This aligns with the Law of Diminishing MRS and the convex shape of indifference curves.
- $MRS_{XY}$ remains the same: This would imply a linear indifference curve, which violates the assumption of diminishing MRS.
- First $MRS_{XY}$ increases but later on $MRS_{XY}$ decreases: This is not the typical behavior for standard indifference curves, which assume diminishing MRS throughout.
Therefore, as consumption of X increases along a typical indifference curve, the $MRS_{XY}$ decreases.
Revision Table: Indifference Curve Concepts
| Concept | Description | Relationship with Consumption of X |
|---|---|---|
| Indifference Curve | Represents combinations of two goods yielding equal utility. | Movement along the curve involves changing consumption of both goods while utility is constant. |
| Marginal Rate of Substitution ($MRS_{XY}$) | Rate at which Y is substituted for X while maintaining utility (absolute slope). | As X increases, $MRS_{XY}$ typically decreases due to diminishing marginal utility. |
| Law of Diminishing MRS | As consumption of one good increases, willingness to give up the other good for it decreases. | Directly causes the $MRS_{XY}$ to decrease as X consumption rises. |
Additional Information: Exceptions and Assumptions
While the diminishing MRS is the standard assumption for typical goods, there are exceptions:
- Perfect Substitutes: The MRS is constant. Indifference curves are straight lines. For example, red pencils and blue pencils (if colour doesn't matter).
- Perfect Complements: The MRS is undefined or zero/infinite at the corner point. Indifference curves are L-shaped. For example, left shoes and right shoes.
The assumption of diminishing MRS reflects the idea that as you consume more of a good, its marginal value relative to other goods tends to fall. This is a key concept in consumer theory and microeconomics.
Important Questions from Indifference curve analysis - Teaching
In the case of consumers equilibrium to be explained through an ordinal approach, when there are two commodities with their prices given and with limited income of the consumer, the following information is required:
a) Price line / budget line
b) Indifference map
c) Point of tangency between IC and budget line
d) Equality of the slopes of IC and budget line
Arrange the information required in the correct sequence and choose the right option from those below
Which one of the following is not the basic property of indifference curves ?
